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Examination of the nanofluid convective instability of vertical constant throughflow in a porous medium layer with variable gravity

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Abstract

In the current article, the impact of varying gravitational field and flow on the beginning of nanofluid convective instability in a permeable medium layer is studied numerically utilizing Galerkin technique. The permeable layer is directed to a regular vertical throughflow and irregular descendent gravitational force which changes with the length from the layer. The influences of three types of gravitational force inconsistency: (a) linear, (b) parabolic, and (c) exponential are examined on the formation of nanofluid convective instability with vanish nanoparticle flux condition at the plates. Results proved that the throughflow factor \(Q\) and gravity inconsistency factor \(\delta\) suspend the start of convective instability, while the nanoparticle Rayleigh-Darcy number \(R_{{{\text{np}}}}\) and the altered diffusivity ratio \({\text{NA}}_{{{\text{nf}}}}\) quick the start of nanofluid convection. The measurement of the convective cells diminishes with \(R_{{{\text{np}}}}\) and \({\text{NA}}_{{{\text{nf}}}}\), while \(Q\), \(\delta\) and the altered nanofluid Lewis number \({\text{Le}}_{{{\text{nf}}}}\) have duel effects on the measurement of convective cells.

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Abbreviations

\(a\) :

Non-dimensional wave number

\(C\) :

Volumetric fraction of nanoparticles

\(D_{B}\) :

Brownian diffusion coefficient

\(D_{\theta }\) :

Thermophoresis diffusion coefficient

\({\hat{\mathbf{e}}}\) :

Unit vector

\(g\left( z \right)\) :

Variable gravity

\(g_{0}\) :

Reference gravity

\(K\) :

Permeability of the porous matrix

\(k_{m}\) :

Aggregate thermal conductivity of the porous matrix

\(L\) :

Height of nanofluid layer

\({\text{Le}}_{{{\text{nf}}}}\) :

Altered nanofluid Lewis number

\({\text{NA}}_{{{\text{nf}}}}\) :

Altered diffusivity ratio

\(P\) :

Pressure

\(Q\) :

Throughflow factor

\(R_{m}\) :

Density Rayleigh–Darcy number

\(R_{{{\text{nf}}}}\) :

Nanofluid Rayleigh–Darcy number

\(R_{{{\text{np}}}}\) :

Nanoparticle Rayleigh–Darcy number

\({\mathbf{v}}\) :

Velocity vector

\(\left( {x,y,z} \right)\) :

Space coordinates

\(\alpha_{m}\) :

Thermal diffusivity

\(\beta\) :

Expansion coefficient

\(\beta_{C}\) :

Nanoparticles volumetric fraction extension coefficient

\(\beta_{\theta }\) :

Thermal extension coefficient

\(\mu\) :

Viscosity

\(\rho\) :

Density

\(\varphi\) :

Volumetric portion of nanoparticle

\(\varepsilon\) :

Porosity of the porous lattice

\(\sigma\) :

Heat capacity ratio

\(\omega\) :

Progress rate of instability

\(\delta\) :

Gravity inconsistency factor

\(\tau\) :

Time

0:

Reference estimate

b :

Basic flow

c :

Critical

m :

Aggregate porous medium

nf:

Nanofluid

np:

Nanoparticles

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Acknowledgements

The authors would like to acknowledge the University of Nizwa for continuous support during this research. Also, the article partially was supported by National Natural Science Foundation of China (No. 71601072) and Key Scientific Research Project of Higher Education Institutions in Henan Province of China (No. 20B110006). Besides, this research was supported by the National Natural Science Foundation of China (Grant Nos. 11971142, 11701176, 11626101, 11871202, 61673169, 11601485).

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Authors and Affiliations

  1. Department of Mathematical and Physical Sciences, University of Nizwa, Nizwa, Oman

    Dhananjay Yadav

  2. Department of Mathematics, Huzhou University, Huzhou, 313000, People’s Republic of China

    Yu-Ming Chu

  3. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, 410114, People’s Republic of China

    Yu-Ming Chu

  4. Yonsei Frontier Lab, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 03722, Republic of Korea

    Z. Li

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  1. Dhananjay Yadav
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Yadav, D., Chu, YM. & Li, Z. Examination of the nanofluid convective instability of vertical constant throughflow in a porous medium layer with variable gravity. Appl Nanosci 13, 353–366 (2023). https://doi.org/10.1007/s13204-021-01700-2

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